Convex solutions of Monge-Ampère equations and systems: Existence, uniqueness and asymptotic behavior

Advances in Nonlinear Analysis

article

Meiqiang Feng¹ 

[1] School of Applied Science, Beijing Information Science & Technology University

关键词: system of Monge-Ampère equations;    convex solutions;    sharp estimates and uniqueness;    existence and asymptotic behavior;    multiparameter;   

DOI  :  10.1515/anona-2020-0139

学科分类：社会科学、人文和艺术（综合）

来源: De Gruyter

【 摘 要 】

In this paper, the equations and systems of Monge-Ampère with parameters are considered. We first show the uniqueness of of nontrivial radial convex solution of Monge-Ampère equations by using sharp estimates. Then we analyze the existence and nonexistence of nontrivial radial convex solutions to Monge-Ampère systems, which includes some new ingredients in the arguments. Furthermore, the asymptotic behavior of nontrivial radial convex solutions for Monge-Ampère systems is also considered. Finally, as an application, we obtain sufficient conditions for the existence of nontrivial radial convex solutions of the power-type system of Monge-Ampère equations.

【 授权许可】

CC BY